This is a suitable starting point for analyzing the probability \(\operatorname{tr}(P_a \rho _{\operatorname{{\mathcal {E}}}})\)  via a polynomial method [1]}.
Let
\(\lbrace K^{\operatorname{{\mathcal {E}}}}_i\rbrace _{i=1}^{2^n 2^m}\) ,
\({\operatorname{{\mathcal {E}}}}(\rho ) = \sum _{i} K^{\operatorname{{\mathcal {E}}}}_i \rho (K^{\operatorname{{\mathcal {E}}}}_i)^\dagger ,\) 
